How to trim a clip affected by speed control?
There are some parameters to check for having audio and video in sync, many others softwares set them automatically, Blender doesn't, so you have to configure them manually.
First of all in the timeline set the sync type to AV Sync (this affects the behaviour during live playback only, it doesn't affect the renders).
Then load the movie in the movie clip editor, read its FPS value and set the same amount in the dimensions properties tab.
Lastly be aware that audio also has to match its sample rate: most commons are 44100 and 48000 (but this is automatically set).
When your audio and video will be in sync you can use the speed control effect strip to manipulate the video as you expect.